Final answer:
The solution requires understanding that the median of a triangle divides the opposite side in a 2:1 ratio. We set up an equation based on given values and solve for x to find that x equals 9.
Step-by-step explanation:
The question is centered on the concept of medians of a triangle and how they divide each other in a specific ratio. In any triangle, the medians intersect at a point which divides them in a 2:1 ratio, with the longer segment being closer to the vertex of the triangle. The student is given CR = 24 and RF = 2x - 6, with R being the point of intersection of the medians (also known as the centroid). To solve for x, we use the fact that RF is twice as long as FR since CR is a median dividing the segment CF into two parts, with CR being twice as long as RF.
Since CR = 24, the entire length of CF is CR + RF which equals to 24 + RF. Knowing CR = 2 * RF, we set up the equation 24 = 2 * (2x - 6), which simplifies to 24 = 4x - 12. Solving for x, we add 12 to both sides to get 36 = 4x, and then divide both sides by 4 to get x = 9.